Question: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$7.50$, and bags of cookies cost $$4.50$, and sales equaled $$58.50$ in total. There were $5$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+4.5y = 58.5}$ ${y = x+5}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+5}$ for $y$ in the first equation. ${7.5x + 4.5}{(x+5)}{= 58.5}$ Simplify and solve for $x$ $ 7.5x+4.5x + 22.5 = 58.5 $ $ 12x+22.5 = 58.5 $ $ 12x = 36 $ $ x = \dfrac{36}{12} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+5}$ to find $y$ ${y = }{(3)}{ + 5}$ ${y = 8}$ You can also plug ${x = 3}$ into $ {7.5x+4.5y = 58.5}$ and get the same answer for $y$ ${7.5}{(3)}{ + 4.5y = 58.5}$ ${y = 8}$ $3$ bags of candy and $8$ bags of cookies were sold.